Farmer John has a block of cheese in the shape of a cube. It lies on the 3-dimensional coordinate plane, extending from (0,0,0) to (N, N, N) (2 \leq N \leq 1000). Farmer John will perform a series of Q (1 \leq Q \leq 2 \cdot 10^5) update operations to his cheese block.

For each update operation, FJ will carve out the 1 by 1 by 1 block of cheese extending from integer coordinates (x, y, z) to (x+1, y+1, z+1), where 0\le x,y,z<N. It is guaranteed that there will exist a 1 by 1 by 1 block of cheese at the location FJ carves. Since FJ is playing Moocraft, gravity does not cause parts of the cheese to fall if cheese below is carved.

After each update, output the number of distinct configurations that FJ can stick a 1 by 1 by N brick in the cheese block such that no part of the brick overlaps with any remaining cheese. Every vertex of the brick must have integer coordinates in the range

[0,N] for all three axes. FJ may rotate the brick however he wants.

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치즈 블록 timer 1s memory 1024MB

#8177
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치즈 블록 1s 1024MB